well, First off, his name is "The Doctor" and no, he doesn't die, he regenerates. in the last Christmas special, the 11th doctor (who was on his last regeneration) was granted another set of regenerations, so we can expect many more seasons of the show ;)
He hasn't died yet.
Doctor Clayton died in 1947.
Doctor Greenwood died in 1951.
The Doctor has died many times, but as a Time Lord, he regenerates into a new incarnation each time.
John McClelland - doctor - died in 1875.
Robert Hale - doctor - died in 1767.
Francis Badgley - doctor - died in 1863.
John Jones - doctor - died in 1791.
Alexander Fleming - doctor - died in 1875.
Jacques d'Amboise - doctor - died in 1603.
Jean Hamon - doctor - died in 1687.
Ian Johnston - doctor - died in 2001.